Problem: $f(x, y) = x^2 \sin(y)$ What is $\dfrac{\partial f}{\partial y}$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $2x \sin(y)$ (Choice B) B $x^2 \cos(y)$ (Choice C) C $2x\cos(y)$ (Choice D) D $2x \sin(y) + x^2 \cos(y)$
Solution: Taking a partial derivative with respect to $y$ means treating $x$ like a constant, then taking a normal derivative. $\begin{aligned} \dfrac{\partial f}{\partial y} &= \dfrac{\partial}{\partial y} \left[ x^2 \sin({y}) \right] \\ \\ &= x^2 \cos({y}) \end{aligned}$ In conclusion, $\dfrac{\partial f}{\partial y} = x^2 \cos(y)$